Abstract

Persistent gamma frequency (30–70 Hz) network oscillations occur in hippocampal slices under conditions of metabotropic glutamate receptor (mGluR) activation. Excessive mGluR activation generated a bistable pattern of network activity during which epochs of gamma oscillations of increasing amplitude were terminated by synchronized bursts and very fast oscillations (>70 Hz). We provide experimental evidence that, during this behavior, pyramidal cell-to-interneuron synaptic depression takes place, occurring spontaneously during the gamma rhythm and associated with the onset of epileptiform bursts. We further provide evidence that excitatory postsynaptic potentials (EPSPs) in pyramidal cells are potentiated during the interburst gamma oscillation. When these two types of synaptic plasticity are incorporated, phenomenologically, into a network model previously shown to account for many features of persistent gamma oscillations, we find that epochs of gamma do indeed alternate with epochs of very fast oscillations and epileptiform bursts. Thus the same neuronal network can generate either gamma oscillations or epileptiform bursts, in a manner depending on the degree of network drive and network-induced fluctuations in synaptic efficacies.

INTRODUCTION

A synchronized neuronal burst, with its accompanying paroxysmal depolarization shift (PDS), is one of the classic hallmarks of many experimental models of epileptogenesis (Prince 1968). Some aspects of the PDS can be understood in terms of synaptic interactions within hippocampal or cortical circuits, especially (but not exclusively) those between principal cells (Gutnick et al. 1982; Miles and Wong 1987; Traub and Wong 1982; Traub et al. 1987, 1996). For example, one can explain in this way the latency to a burst after a small stimulus, and also the shape of intracellular potentials, because they are altered by varying levels of synaptic inhibition and recurrent excitation. Consideration of chemical synaptic interactions alone, however, does not explain the high-frequency oscillations that can be superimposed on the PDS (Grenier et al. 2003; Schwartzkroin and Prince 1977; Snow and Dudek 1984; Wong and Traub 1983). Nor is it always apparent how an epileptiform burst arises, apparently spontaneously, out of normal or nearly normal background activity, as can occur in vivo. It is also not known if, in vivo, the appearance of synchronized bursting reflects an alteration in one or more time-dependent system parameters.

Nanomolar concentrations of kainate induce gamma frequency (30–70 Hz) oscillations in hippocampal slices from wild-type mice. In slices from connexin36 knockout mice, however, the drug elicits gamma oscillations that are of reduced power compared with wild-type (Hormuzdi et al. 2001); a detailed network model suggests that the reduced power results because fewer interneuron action potentials occur in conditions where the interneurons are electrically uncoupled (Traub et al. 2003b) (connexin36 is a neuronal gap junction protein that is primarily involved in the electrical coupling of interneurons). In addition to gamma oscillations, synchronized epileptiform bursts also occur in the connexin36 knockout (but not wild-type) in the presence of kainate (Pais et al. 2003). Very fast oscillations (VFOs; >70 Hz) are superimposed on the bursts. Population activity (both gamma oscillations and bursts) in the knockout depends on synaptic receptors (including GABAA) and on gap junctions (Pais et al. 2003; Traub et al. 2003b). Because electrical coupling between interneurons is largely abolished in the connexin 36 knockout (Hormuzdi et al. 2001), the effect of gap junction blockers in the knockout is presumed to occur via an action on putative axonal gap junctions (Schmitz et al. 2001b; Traub et al. 2003b). The connexin 36 knockout mouse therefore raises questions concerning how chemical synaptic and gap junctional mechanisms are able to cooperate in epileptogenesis.

In this study, we developed an experimental model, using the metabotropic glutamate receptor agonist (S)-3,5-dihydroxyphenylglycine (DHPG), that allows study, in wild-type mice, of gamma oscillations intermixed with epileptiform bursts and VFOs. DHPG has previously been shown to be epileptogenic in vivo when injected into the cerebral ventricles (Camon et al. 1998). The compound prolongs in vitro hippocampal epileptiform bursts induced by disinhibition and can alter burst frequency (Merlin 1999, 2002 in guinea pig slices; Sayin and Rutecki 2003 in rat slices). DHPG has also been shown to induce in vitro epileptiform activity on its own in adult rat hippocampal slices (Sayin and Rutecki 2003) or in mouse hippocampal slices (Zhao et al. 2004), using concentration of 100 and 50 μM, respectively. Gamma oscillations and VFOs were not studied in these previous epilepsy investigations.

We first present experimental data supporting the existence of two relevant time-dependent synaptic conductance changes that occur during and between epileptiform bursts: 1) after a DHPG-induced synchronized epileptiform burst, population excitatory postsynaptic potentials (EPSPs) in pyramidal cells are almost completely absent and then gradually potentiate until the next burst occurs; 2) in contrast, phasic excitation of interneurons gradually—but somewhat sporadically—declines from one synchronized burst to the next. We show that a simulation model of persistent gamma oscillations, developed to study kainate-induced gamma oscillations (Traub et al. 2003b), can reproduce the basic experimental data on DHPG-induced bursting, when corresponding time-dependent changes in synaptic conductances are also incorporated into the model in a phenomenological manner. [We are aware, however, that not all experimental models of persistent gamma oscillations are identical in detail; i.e., kainate and DHPG do not necessarily induce gamma oscillations identically in every respect (Pálhalmi et al. 2004).] The resulting simulation model generates periods of gamma oscillation and epileptiform bursts in alternating fashion, as occur experimentally. As in our previous work, putative electrical coupling between pyramidal cell axons here plays a crucial role in the very fast oscillations as well as the gamma oscillations (Traub et al. 2000, 2003a,Traub et al. 2003b).

METHODS

Experimental methods

Adult male C57 mice (∼3–6 mo) were anesthetized with inhaled isoflurane followed by injection of ketamine (100 mg/kg, im) and xylazine (10 mg/kg, im). After the abolition of all pain reflexes the animals were perfused intracardially with ∼25 ml of modified artificial cerebrospinal fluid (ACSF), which was composed of (in mM) 252 sucrose, 3.0 KCl, 1.25 NaH2PO4, 24 NaHCO3, 2.0 MgSO4, 2.0 CaCl2, and 10 glucose. After brain removal, 450-μm-thick horizontal slices were cut. Slices were trimmed and transferred to a holding chamber where they were maintained at room temperature at the interface between normal ACSF (where sucrose was replaced with 126 mM NaCl) and humidified 95% O2-5% CO2. For recording, slices were transferred to an interface chamber maintained at 34–35°C. Field gamma oscillations and burst discharges were generated by bath application of DHPG (10–100 μM; Tocris Cookson).

Extracellular recording electrodes were filled with ACSF (resistance 1–4 MΩ). All field data were taken from area CA3 stratum pyramidale. Intracellular recordings were taken from CA3 pyramidal neurons and fast-spiking CA3 s. pyramidale interneurons using electrodes filled with 2 M potassium acetate or methysulphate (resistance 40–90 MΩ). Frequency and power of gamma oscillations were obtained from power spectra. Mean recurrent EPSP amplitudes were obtained by averaging EPSP amplitudes (in cells with membrane potential adjusted to near −70 mV) occurring in a 0.5-s window time-locked to the initiation of a burst. Median data from three interburst intervals per pyramidal cell were used to generate a global average (n = 5 experiments). The more regular pattern of EPSPs in interneurons, compared with pyramidal cells, meant that averaging over 0.5 s was not necessary. Interneuron EPSP averages were taken for each gamma period (working back from the initiation of each burst) for three interburst intervals per cell. Interneuron EPSPs were also recorded in cells held near −70 mV. Inhibitory postsynaptic potentials (IPSPs) in interneurons and pyramidal neurons were recorded in cells held near −30 mV. The median values from this analysis were used for the global mean (n = 5 experiments). Both for experiments and simulations, results are expressed as mean ± SE, and statistical significance was determined with a Student's t-test. A significance level of P < 0.05 was chosen.

Simulations

Network structure was similar (in essentials) to that used by Traub and Bibbig (2000), with the addition of dendritic gap junctions (as in Traub et al. 2003b) and other modifications described below. The present network had, as before, 3,072 pyramidal cells (e-cells) and 384 interneurons (i-cells: 96 basket cells, 96 chandelier cells, 192 dendrite-contacting interneurons). Each pyramidal cell was multicompartment (Traub et al. 1994) but with the axon extended from 5 to 10 compartments (each 75 μm long). gCa and gK(AHP) densities were halved compared with the original paper (Melyan et al. 2002). Each interneuron was also multi-compartmental (Traub and Miles 1995), but with reduced active conductance densities in the dendrites. There was a random current bias of −0.15 to −0.05 nA to pyramidal cells, and a tonic excitation of 5.5 nS to each of seven compartments in the apical dendrites (reversal 60 mV positive to resting potential). Each interneuron received a randomly chosen tonic excitatory conductance of 1 to 2 nS to each of four compartments in the proximal dendrites. In addition, Poisson-distributed ectopic axonal action potentials occurred, averaging 1 Hz per axon in pyramidal cells and 0.2 Hz per axon in interneurons. [Experimental evidence indicates that kainate can directly increase the excitability of axons and presynaptic terminals in principal cells and interneurons (Schmitz et al. 2001a; Semyanov and Kullmann 2001) and also that spikelets are observed during persistent gamma oscillations in several brain areas (Cunningham et al. 2004a,Cunningham et al. 2004b; Fisahn et al. 2004).] Membrane potentials in the model neurons are all expressed relative to resting potential (Traub et al. 1994).

We did not simulate mossy fiber inputs to the model pyramidal neurons, because we have not observed spontaneous gamma oscillations in the dentate gyrus under conditions where the CA3 region exhibits persistent gamma oscillations (SK Towers, MA Whittington et al., and EH Buhl et al.1998, unpublished data).

CHEMICAL SYNAPTIC CONNECTIVITY.

Each pyramidal cell (e-cell) received inputs from 30 pyramidal cells and 80 interneurons (20 basket cells, 20 chandelier cells, 40 dendrite-contacting cells). Each interneuron (i-cell) was excited by 150 pyramidal cells and inhibited by 60 interneurons (20 basket cells, 40 dendrite-contacting cells). Excitatory connections were to mid-basilar and apical dendrites of pyramidal cells and mid-dendrites of interneurons. Chandelier cells inhibited the first axonal compartment of pyramidal cells; basket cells inhibited the soma and proximal dendrites of principal cells. Inhibitory connections were in the dendrites of interneurons. AMPA and GABAA receptors were simulated. Unitary pyramidal excitatory postsynaptic currents (EPSCs) were (in nS, and t in ms) scaling constant × 2.1 × texp(−t/2), and interneuron EPSCs were scaling constant × 0.5 × texp(−t). The scaling constants are time-dependent; they depend on the identity of the presynaptic axon for interneuron EPSCs, but do not depend on this identity for pyramidal EPSCs. The unitary inhibitory postsynaptic currents (IPSCs) decayed with a time constant 10 ms and peaked at 1 or 2 nS on pyramidal cells (2 nS in the shown simulations), 1 or 2 nS for basket-to-interneuron connections, and 0.1 or 0.2 nS for other interneuron–interneuron connections (2 and 0.2 nS in the shown simulations).

RULES FOR TIME DEPENDENCE OF THE EPSC SCALING CONSTANTS (HABITUATION).

The pyramidal EPSC scaling constant (as noted above, the same for all pyramidal cell axons at any given time) followed a phenomenological time-dependency scheme similar to that used by Staley et al. (1998) (see also Yee et al. 2003): a “population burst” set the scaling constant to 0.0 (in effect, synaptically disconnecting the pyramidal cells); the scaling constant then relaxed back toward 1.0 with a time constant measured in seconds (we used 1.5 and 2.5 s; 2.5 s in the shown simulations). The problem is to define a population burst that the program can recognize as the system is evolving. We used a simple definition: a population burst was defined to occur when 75,000 pyramidal cell axonal spikes occurred within 250 ms. The 75,000 threshold was found to be workable after testing a variety of values in preliminary simulations. The initial value of the e-to-e scaling constant was 0.9, a value that favored the occurrence of a population burst at the start of a simulation.

The interneuron EPSC scaling constants evolved individually for each presynaptic pyramidal cell axon. Let khabituation be some small positive integer (≤10), predetermined for each simulation. In the shown simulations, khabituation was 7. For each given axon, the scaling constant is set to 0.0 when two conditions hold: 1) khabituation action potentials have occurred in the axon in the last 100 ms and 2) the scaling constant has not been set to 0.0 for some interval (usually 500 ms). Once the scaling constant has been set to 0.0, it relaxes exponentially back to 1.0 with a time constant of 400 ms. The initial values of the interneuron EPSC scaling constants were all 0.1, a small value that also favored the occurrence of a synchronized burst at the start of a simulation.

While it is impossible to use our model to define unique values for the synaptic conductances to replicate the experimental data, it is still the case that the conductance parameters are constrained and that some of the interdependencies make physical sense. Thus if gamma oscillations are to occur, unitary IPSCs must be sufficiently large, and e→i conductances must be large enough for at least some portion of the interburst cycle. Once IPSCs are made large enough (and assuming they are time independent), which in turn put constraints on e→e conductances, the latter must be large enough at one part of the cycle so that a burst can be initiated, in the time as e→i conductances collapse (see Figs. 1 and 6); however, if e→e conductances are too large after the burst, they interfere with the generation of the gamma oscillation (Traub et al. 1997, 2000). The time constant for increasing e→e conductances is a major determinant of the interburst interval. Given values and time constants for e→e conductances, the parameters for e→i habituation become constrained: if khabituation is too large, bursts do not occur. If khabituation is too small, there cannot be a period of (relatively) sustained gamma oscillation.

GAP JUNCTIONS.

Gap junctions were located in pyramidal cell axons in the compartment centered 187.5 μm from the soma (Schmitz et al. 2001b) and on interneuron dendrites in a compartment centered 85 μm from the soma (Traub et al. 2001a). Gap junctions (axonal or dendritic) could only form between neurons with soma <200 μm apart. There were a total of 2,458 axonal gap junctions, randomly distributed (subject to the spatial constraint), so that each pyramidal axon contacted, on average, 1.6 other axons; in addition, no axon was allowed to be coupled to more than four others. There were a total of 384 dendritic gap junctions, also randomly distributed subject to the 200-μm spatial constraint, so that each interneuron contacted, on average, two other interneurons; no interneuron could be electrically coupled to more than four others. For interneuron gap junctions, there was an additional constraint: no junctions could form between basket cells (or chandelier cells) and dendrite-contacting interneurons (Gibson et al. 1999). Axonal gap junction conductance was 2.33 nS, a value that could allow an action potential to cross from axon to axon. For interneurons, we used values of 0.00 to 1.97 nS in different instances. In the simulations shown here, the interneuron gap junction conductance was 0.0 nS.

We show average activity of the network with a rough approximation to a field potential: minus the average somatic potential of 224 nearby pyramidal cells. We also used potentials at selected compartments of individual cells (dendrites, soma, or axon), total excitatory and inhibitory synaptic conductances in selected neurons, along with signals that reflect the average scaling factors for selected synaptic conductances (e-to-e and e-to-i). A fast Fourier transform (FFT) of the field was calculated with a sliding window (512 data points or 96 ms) every 4.67 ms, and the frequency at which peak power occurred was stored. This frequency-of-peak-power, as a function of time, allows one to identify readily periods of gamma oscillation in the field, as well as the occurrence of epileptiform bursts: the latter appear as a brief “spike” of VFO, followed by transient slowing of oscillation frequency (e.g., Fig. 5).

Programs were written in FORTRAN augmented with instructions for parallel computing. Initial simulations were run under AIX using 12 processors of two different IBM SP2 parallel computers. In the computer with power-2 processors, it took about 6.2 h to simulate each second of network activity. With power-3 processors, it took about 3.1 h. Later simulations, of 15–17 s of activity, were run on 12 central processing units (e1350 Blade 1, 2.8 GHz) in a Linux cluster (an IBM e1350). On the Linux cluster, it took about 18 h to simulate 10 s of network activity. For programming and other details, please contact R. D. Traub.

Transition to burst is preceded by a gradual increase in recurrent excitation. A: somatic recordings from a CA3 pyramidal cell during DHPG-induced gamma/burst activity. Cell injected with −0.1 nA current to give a mean resting membrane potential of −70 mV. Excitatory postsynaptic potentials (EPSPs) increase gradually within the interburst interval. Note the large depolarizing envelope associated with each burst (*). B: example interburst interval, from cessation of 1 burst to initiation of the next. Recording was high-pass filtered off-line (>0.5 Hz) to allow for analysis of EPSP amplitude. Graph shows pooled data (n = 3 interburst intervals from n = 5 CA3 pyramidal cells) of average EPSP amplitude over 0.5-s intervals time locked to the initiation of a burst.

In contrast to the observed increase in phasic excitatory drive to pyramidal cells, a gradual decrease in phasic drive to fast spiking, s. pyramidale interneurons was seen (Fig. 3). At −70 mV, somatic interneuron recordings revealed contrasting membrane potential changes to those seen during bursts in pyramidal cells. Field potential bursts corresponded only to a small depolarization, no change, or a hyperpolarization of interneurons (Fig. 3A, *). Mean membrane potential depolarization during a burst was 2.2 ± 0.8 mV, smaller than the 9.6 mV depolarization seen in pyramidal cells, P < 0.05 (n = 5). In addition, a different profile of changes in phasic excitation was seen during interburst intervals. Pyramidal cell EPSPs potentiated significantly over the interburst period, whereas interneuron EPSPs showed brief (90–150 ms) periods of near-complete habituation toward the initiation time of the next burst (Fig. 3B). Period-by-period averages (n = 3 bursts/cell, n = 5 cells), working back from burst initiation, revealed a sharp drop in mean interneuron EPSP before burst initiation (Fig. 3C). Interneuronal EPSP amplitude 5 s before a burst was 10.5 ± 2.1 mV, whereas immediately before a burst, EPSP amplitude was 2.4 ± 0.1 mV (P < 0.05, n = 5). The decline in amplitude of EPSPs in interneurons over the course of the interburst interval was unlikely to be caused primarily by a shunt in interneurons developing over the interburst interval. Such a shunt would be expected to produce alterations in IPSPs (in interneurons) in parallel with the EPSP alterations, but this was not observed (see Fig. 4).

Burst initiation is preceded by a failure of phasic excitation to interneurons. A: example trace from a CA3, fast spiking, s. pyramidale interneuron injected with −0.2 nA current to give a mean membrane potential of −70 mV. Bursts are followed by large amplitude (about 15–20 mV) trains of EPSPs that decay erratically in amplitude until initiation of the next burst. Action potentials are attenuated for clarity. Note the near absence of a depolarizing envelope during the burst (*, cf. Fig. 2A). B: single interburst interval showing the erratic pattern of EPSP habituation. C: (left) plot of EPSP amplitude per gamma period working back from the point of burst initiation for a single interneuron. Note the transient abolition of phasic EPSPs occurring ∼1–2 s before the final failure of phasic drive preceding the burst. Right: mean ± SE (n = 5) for the period by period change in interneuron EPSP amplitude averaged with respect to burst initiation.

Phasic inhibitory drive to interneurons and pyramidal cells is disrupted preceding a burst. A: example pyramidal cell recording during interburst interval at −30-mV membrane potential. Phasic inhibitory drive gradually decays before a small amplitude ripple of inhibitory postsynaptic potentials (IPSPs) is seen before burst initiation (shown on expanded trace, taken from main trace as indicated by the bar). B: example interneuron recording during interburst interval at −30-mV membrane potential. Phasic inhibitory drive to the interneuron remains stable until ∼100 ms before burst initiation, whereupon a high-frequency barrage of smaller IPSPs at very fast oscillation frequency is seen (expanded trace taken from the main trace as indicated by the bar).

The increase in recurrent excitation and decrease in phasic drive to interneurons were accompanied by changes in the pattern of IPSPs onto principal cells. As the phasic drive to interneurons decreased, there was a concomitant, gradual decrease in gamma frequency inhibitory postsynaptic potentials observed in pyramidal cell somatic recordings (Fig. 4A). At a membrane potential of −30 mV, average IPSP amplitude 5 s before burst initiation was 8.7 ± 1.2 mV, whereas immediately preceding a burst, IPSP amplitude was 2.5 ± 0.6 mV. In three of five pyramidal cell recordings, burst initiation was also immediately preceded by a change in frequency of IPSPs (Fig. 4A). IPSPs reduced in size rapidly, and the frequency of occurrence increased to over twice gamma frequency (70–94 Hz). In contrast, IPSP amplitudes in interneurons remained relatively constant throughout the interburst interval (mean amplitude, 1.6–2.2 mV at −30-mV membrane potential; n = 3). However, 100 ms immediately preceding burst onset, a rapid change in inhibitory drive to interneurons was seen. Instead of a gamma frequency sequence of brief depolarizations followed by sharp IPSPs (see Tamás et al. 2000), a switch to high-frequency membrane potential oscillations at VFO frequency was seen (Fig. 4B).

Model results

It has previously been shown that models with principal cell axonal gap junctions (with or without interneuron dendritic gap junctions), also containing chemical synapses, can generate network gamma oscillations that possess attributes appropriate to experimental persistent gamma oscillations (Traub et al. 2000, 2003b). Examples of such attributes are as follows: 1) dependence of the oscillation on AMPA receptors, GABAA receptors, and gap junctions; 2) higher firing rates for interneurons than for principal cells; and 3) a slight leading by the average pyramidal cell signal relative to the average interneuron signal. With time-varying modifications in EPSCs in interneurons and pyramidal cells, dependent on the history of simulated network activity (see methods), periods of gamma oscillations alternate with synchronized bursts as in the experiments described above (cf. also Pais et al. 2003).

Figure 5 shows the simulated “field,” along with the frequency at which peak power occurred, in the Fourier power spectrum (calculated in a sliding window of 96-ms width). Mostly the field oscillation is at gamma frequency (the horizontal red line indicating 40 Hz). Synchronized bursts (*) occur as brief epochs of a VFO (>70 Hz), each followed by a brief epoch of oscillation suppression (cf. Figs. 1 and 2). The interburst period was 2–4 s, somewhat shorter than the experimental period of about 5 s. The interburst interval could be lengthened, however, by slowing the time constant for recovery of EPSCs after a burst (data not shown).

Gamma oscillations can evolve into epileptiform bursts when pyramidal→pyramidal and pyramidal→interneuron habituation are present: simulation. A: 11-s train of data showing the field (top), and the frequency at which the power spectrum (in a sliding 96-ms window) has its peak value (bottom). Red horizontal line marks 40 Hz. Most of the activity consists of gamma oscillation (at or near 40 Hz). Around the time of population bursts (*), there is very fast oscillatory activity (VFO), followed by transient slowing of field activity. B: expanded trace of the 2nd interburst interval in A. Note that the period between simulated epileptiform bursts is shorter than in the experiments.

As Fig. 6 shows, simulated pyramidal cell EPSCs increase more-or-less monotonically during the interburst interval, as occurs experimentally (Fig. 2). Interneuron EPSCs fluctuate from interval to interval in an individual cell (cf. Fig. 3), but on average, begin to decline noticeably some hundreds of milliseconds before the synchronized burst (cf. bottom traces in Fig. 6 with bottom right of Fig. 3). Such a decline in phasic excitation of interneurons in the model is causally related to the occurrence of the population burst. It is the case, however, that if pyramidal cell EPSCs are made sufficiently large (>1.5 times as large as used here), the model can generate cyclically repeating bursts without habituation of interneuronal EPSCs (data not shown).

Time-dependent alterations inEPSCs: simulation. A: for 1 interburst interval, traces are as follows: total AMPA receptor-mediated conductance in a model pyramidal cell; the mean (averaged over all pyramidal cells) of the e/e (pyramid-to-pyramid) EPSC scaling factor (see methods); the total AMPA receptor-mediated conductance in a model interneuron; and the mean (averaged over all presynaptic pyramidal cells) of the e/i (pyramid-to-interneuron) EPSC scaling factor. Note that the temporal increase of pyramidal cell EPSCs is more regular than for interneurons and that interneuron EPSCs start to decline before the next population burst (Figs. 1 and 2). B: same traces on an expanded time scale, showing the interval just before a burst. Gamma oscillations start to become disorganized just before the burst. Same simulation as Fig. 5.

Firing behavior of individual neurons in the model consisted of two phases, as in the experiments (Figs. 2 and 3). Thus Fig. 7 shows that, during gamma oscillations, there are rhythmic synaptic potentials in both cell types, with the interneuron firing more than the pyramidal cell (the degree of somatic firing was, however, sensitive to membrane potential in each cell type; data not shown). Pyramidal cell bursts (*) were associated with small intracellular depolarizations (<5 mV) and increased firing in pyramidal cells but decreased firing in model interneurons. Experimentally, suppression of firing was seen in some interneurons during a burst (e.g., Fig. 3A), but not in others.

Firing behavior of model neurons. A: an interburst interval, with bursts marked by *. Note the limited depolarization and firing of the pyramidal cell during the burst and the suppression of firing in the interneuron. B: expanded time scale corresponding to brackets. Subthreshold oscillation in the pyramidal cell and frequent interneuron firing are qualitatively similar to patterns seen in carbachol- and kainate-induced persistent gamma oscillations (Fisahn et al. 1998; Hormuzdi et al. 2001; Traub et al. 2000, 2003b). This particular pyramidal cell exhibits numerous spikelets on the peaks of the gamma waves (cf. Cunningham et al. 2004a,Cunningham et al. 2004b and Fisahn et al. 2004). Same simulation as Fig. 5.

Pais et al. (2003) showed that, during kainate-induced synchronized bursts (alternating with periods of gamma in hippocampal slices from connexin36 knockout mice), runs of pyramidal cell spikelets could be observed. Runs of spikelets were also observed in the present simulations (Fig. 8), provided a pyramidal cell was chosen that was not too depolarized (which would cause each spikelet to turn into a full action potential) and provided that the pyramidal cell resided on the “large cluster” in the axonal electrical network. [The notion of “large cluster” is described in Traub et al. (1999, 2001b, 2002).] In the case of the model, spikelets were antidromically driven (Fig. 8), as occurs in models of persistent gamma oscillations (Cunningham et al. 2004b; Fisahn et al. 2004; Traub et al. 2000) and in at least some experimental paradigms (Schmitz et al. 2001b). It has not proven possible, to our knowledge, to show experimentally an antidromic origin for spikelets during an epileptic burst.

Antidromically elicited spikelets occur in pyramidal cells during a population burst (simulation). Illustrated pyramidal cell was hyperpolarized with a −1.0-nA current. Note the occurrence of frequent spikelets (some marked with *) during the burst. (Spikelets occur also before and after the burst in this model neuron at lower frequency). The axon fires continuously during the burst. A similar run of spikelets during a population burst was observed in kainate-induced bursts in hippocampal slices taken from a connexin36 knockout mouse (Pais et al. 2003). Same simulation as Fig. 5.

IPSCs in the model, in pyramidal cells and in interneurons, also resembled experimental patterns, at least qualitatively (Fig. 9). Specifically, gamma oscillatory conductances are seen in both cell types throughout almost all of the interburst intervals, with breakup of the oscillatory pattern just before (<100 ms) the burst.

IPSCs occur rhythmically until just before a burst (simulation). A: total GABAA receptor–mediated conductance in a model pyramidal neuron over the course of an interburst interval; in an interneuron; and the simultaneous field. B: traces during the thick bar are expanded to show disorganization of the oscillation just before the burst. Same parameters as Fig. 5, but with slightly larger scaling of pyramid-to-pyramid EPSCs (1.15 times).

DISCUSSION

In this paper, we showed that sufficiently high concentrations of the metabotropic glutamate receptor agonist DHPG can induce repeating epileptiform population bursts (period about 5 s), interspersed with epochs of gamma oscillation, epochs that resemble sustained (or “persistent”) gamma oscillations induced by lower concentrations of DHPG, carbachol, and kainate. During the interburst interval, EPSCs gradually and more-or-less smoothly increase in pyramidal neurons, whereas EPSCs in interneurons fluctuate but tend to decrease in the hundreds of milliseconds before a burst. By taking an established network model of persistent gamma oscillations (Traub et al. 2003b) and adding time-dependent modifications in EPSC strengths, we have obtained a model that exhibits qualitatively similar population behavior to what is seen experimentally. The model does not account for the molecular and biophysical mechanisms that underlie the time-dependent synaptic alterations. The model does, however, allow one to make sense of how—given that the synaptic alterations do, in fact, occur—the network is able to alternate between gamma and bursting modes of behavior.

Experimental precedents

There are precedents in the experimental literature for some of our findings. 1) Gamma oscillations before epileptic seizures have been observed in rats given kainate intravenously (Medvedev et al. 2000) and occurring spontaneously in humans with focal epilepsies (Fisher et al. 1992). 2) Loss of interneuron nerve terminals (Ribak et al. 1979) and excitatory deafferentation of interneurons—the “dormant basket cell hypothesis” (Bekenstein and Lothman 1993; Sloviter et al. 2003)—have been proposed as permanent, structural alterations that could lead to disinhibition and promote epileptogenesis. We note, however, that permanent, structural loss of excitation to interneurons is not what we observed in this study; rather, we observed repeating, transient loss of excitation to interneurons. Transient, functional excitatory deafferentation of interneurons seems plausible after a period of gamma oscillation, given that gamma frequency EPSPs exhibit synaptic depression in fast spiking interneurons (Beierlein et al. 2003; Pouille and Scanziani 2004; Thomson and West 2003). 3) Concerning the cessation of synchronized bursts—in contrast to their initiation—there is evidence that a loss of recurrent synaptic excitation contributes to the termination of synchronized population bursts in the CA3 region of the hippocampus (Staley et al. 1998).

As far as we are aware, the first example of a robust and continuing alternation between gamma epochs and epileptiform bursts was in the study of Pais et al. (2003), in which hippocampal slices from connexin36 knockout mice (Hormuzdi et al. 2001) were bathed in kainate. Pais et al. (2003) found that both the epileptiform bursts and the gamma oscillations were eliminated by the gap junction blocking compound carbenoxolone. Because interneuron electrical coupling in the connexin36 knockout mouse seems nearly absent (Deans et al. 2001; Hormuzdi et al. 2001), we have interpreted this finding to mean that putative axonal coupling between pyramidal cells contributes to persistent gamma oscillations (Traub et al. 2003b) and perhaps also to the bursts.

DHPG experimental model

We wished to examine gamma alternating with bursts in a line of wild-type mice, but kainate in nanomolar–micromolar concentrations did not lead to epileptiform bursts in wild-type mice (Pais et al. 2003). Given that population EPSCs in interneurons are larger in connexin36 knockout mice than in wild-type mice (Hormuzdi et al. 2001), we hypothesized that, in the knockout mice, pyramidal cell-to-interneuron synaptic connections release more glutamate than in wild-type mice; we suggest that the hypothesized enhanced glutamate release renders the synapses more susceptible to synaptic habituation, thus predisposing hippocampal networks to epileptogenesis. We have, as yet, no direct evidence for this hypothesis; however, even if it is true, such a mechanism does not seem sufficient to generate bursts in kainate with wild-type slices. As these data show, however, DHPG does permit gamma oscillations to occur, and at high enough concentrations and by whatever molecular mechanism allows sufficient habituation for epileptiform activity to intervene periodically. Possibly, differential activation of interneuron types could explain why kainate and DHPG lead to contrasting results; such differences have been postulated to occur in comparing carbachol- and DHPG-induced gamma oscillations (Pálhalmi et al. 2004).

Why does the network cycle between gamma oscillations and bursts?

Phasic excitation of interneurons seems to be necessary for most, if not all, persistent gamma oscillations to occur (Fisahn et al. 1998). When such phasic excitation becomes too small, one would expect persistent gamma to be less stable (note that we are considering persistent gamma, as induced by carbachol, kainate, or DHPG, and not interneuron network gamma that occurs during blockade of phasic glutamatergic excitation (Traub et al. 2004; Whittington et al. 1995)). Furthermore, although possibly of secondary importance, modeling suggests that when recurrent excitation between pyramids is too large, this will also destabilize persistent gamma, whereas having minimal recurrent excitation between pyramids is not detrimental to persistent gamma (Traub et al. 2000). [A recent experimental study, using current source density analysis, also suggests that persistent gamma occurs in situations where recurrent pyramidal cell excitation is minimal (Mann et al. 2005).] Thus one would expect gamma oscillations to occur in the network when phasic excitation of interneurons is large enough and phasic excitation of pyramidal cells is small enough.

Conversely, synchronized bursts tend to occur when recurrent excitation between pyramidal cells is sufficiently large and/or aided by electrical coupling (Traub et al. 1999) and is not too suppressed by recurrent inhibition (Traub et al. 1987). The time-dependent alterations in EPSCs act to cycle the system between parameter regimes that favor one or the other type of collective behavior. Putative electrical coupling between the pyramidal cells is expected to favor both the persistent gamma (Traub et al. 2003a,Traub et al. 2003b) and the synchronized bursts (Traub et al. 1999).

Are depolarizing GABAA responses important?

We cannot definitively rule out some contribution of depolarizing GABA responses to the synaptic potentials that we have recorded (Kaila et al. 1997; Perkins and Wong 1997; Staley 2004). A number of factors, however, make it unlikely (in our opinion) that depolarizing GABA plays a major role: 1) synaptic potentials are large in cells recorded at −30 mV (Fig. 4); 2) interneuron depolarization is limited during a burst (average, 2.2 mV), so that large increases in burst-associated interneuron firing are not expected (and indeed were not observed; it is problematic, therefore to explain how the required excessive GABA release would occur); 3) burst duration was short (∼150 ms), unlike the prolonged burst discharges typically associated with depolarizing GABA synaptic potentials (cf. Fujiwara-Tsukamoto et al. 2003); and 4) our model omits depolarizing GABA effects, yet compares extremely well with the experimental data.

Possible clinical relevance

Our results may be relevant in clinical situations where repetitive stimulation of some brain region leads to seizure activity. For example, photosensitive epilepsy in humans, especially in Janz syndrome (juvenile myoclonic epilepsy), has long been recognized (Aso et al. 1994; Hishikawa et al. 1967); likewise, there is an inherited photosensitive epilepsy in baboons (Meldrum et al. 1975). Repetitive photic stimulation can, in susceptible individuals, elicit paroxysmal EEG responses that outlast the stimulation, with stimulation frequencies 15–20 Hz generally being most effective (Topalkara et al. 1998). While 15–20 Hz is a frequency range somewhat slower than occurs during persistent gamma oscillations, it is still possible that photic driving leads to failure of synaptic excitation of interneurons (at least in certain individuals), along with intense excitation of principal cells. In addition, seizures are elicited in some individuals by specific cortical activities, including reading (Bickford et al. 1956) and mental arithmetic (Ingvar and Nyman 1962). It is possible that such seizures could be related to cortical gamma oscillations, given that gamma oscillations occur in the motor cortex as part of motor planning in monkeys (Murthy and Fetz 1992) and in the visual cortex in response to visual stimulation (Gray and Singer 1989).

GRANTS

This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-44133-01 to R. D. Traub, the Medical Research Council (UK) to E. H. Buhl and M. A. Whittington, the Schilling Foundation, and the Deutsche Forschungs Gemeinschaft to H. Monyer.

Acknowledgments

We thank R. Walkup, W. Weir, and P. Mayes (all of IBM Corp.) for help with parallel computing and Dr. Katherine L. Perkins for helpful discussions.

Footnotes

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.